We consider a cognitive radio network with multiple primary users (PUs) and one secondary user (SU), where a spectrum server is utilized for scheduling the SU to transmit over one of the PU channels opportunistically. One practical yet challenging scenario is when both the PU occupancy and the channel fading vary over time and exhibit temporal correlations. Little work has been done for exploiting such temporal memory in the channel fading and the PU occupancy simultaneously for opportunistic spectrum scheduling. Further, the scenario where PU occupancy possesses a long temporal memory has been underexplored as well. By casting the problem as a partially observable Markov decision process, we aim to understand the intricate tradeoffs resulting from the interactions of the two sets of system states (i.e., channel fading and PU occupancy) and the impact of the associated temporal memory. We identify and illustrate a set of multi-tier tradeoffs that go beyond the classic 'exploitation vs. exploration' tradeoff. For certain special cases, we establish the optimality of a simple greedy policy. To build a more comprehensive understanding, we then introduce a full-observation genie-aided system that helps in decomposing the tradeoffs in the original system into multiple layers, which we examine progressively. Numerical examples indicate that the optimal scheduler in the original system, with observation on the scheduled channel only, achieves a performance very close to the genie-aided system. In addition, the optimal policy in the original system significantly outperforms randomized scheduling, as well as a policy that explores memory in one system state only, pointing to the merit of jointly exploiting the temporal correlation structure in both channel fading and PU occupancy.